Standard methods to do volatility forecasting are typically built upon GARCH-type models, these models' abilities to forecast the absolute magnitude and quantiles or entire density of squared financial log-returns (i.e., equivalent to volatility forecasting to some extent)Squared log-returns are an unbiased but very noisy measure of volatility pointed out by [1]}. Additionally, [2]} showed that using squared log-returns as a proxy for volatility can render a correct ranking of different GARCH models in terms of a quadratic loss function. were shown by [3]} using Dow Jones Industrial Index. Later, many studies about comparing the performance of different GARCH-type models on predicting volatility of financial series were conducted [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}. Some researchers also tried to develop the GARCH model further, such as adopting smoothing parameters or adding more related information to estimate model [11]}, [12]}, [13]}, [14]}. For modelling the proper process of volatility during fluctuated period, researchers also developed different approaches to achieve this goal, such as [15]} applied time series models with stable and tempered-stable innovations to measure market risk during highly volatile period; [16]} applied a
fractionally integrated time-varying GARCH (FITVGARCH) model to fit volatility; [17]} developed a Bayesian method to estimate time-varying analogues of ARCH-type models for describing frequent volatility changes. Although there are many different types of GARCH models, it is a difficult problem to determine which single GARCH model outperforms others uniformly since the performance of these models heavily depends on the error distribution, the length of prediction horizon and the property of datasets.
